My iOS app does a lot of different requests to a Web service. Each request is a call to a method of a ConnectionManager object. When the response arrives from the Web service, a delegate's method is called to notify an interested receiver. Moreover, to maintain the session active, a polling every X seconds is required.

Said so, in your opinion it is better if ConnectionManager is a Singleton or not?

The singleton is simpler (because I do not have to pass a ConnectionManager's reference to all those who need to do a request to the Web service or I do not have to create more ConnectionManagers). Moreover, it is easy to handle the issue of polling: I just add two methods startPolling and stopPolling on the ConnectionManager. But I do not like to use the delegates with a singleton (because there can be only one delegate, and what happens if a response comes when there is not one set?) and at the same time I do not like to use the notifications. I do not like the singleton, too :)